Mixed Positive-Bounded Balanced Truncation

Reducing the order of positive real and bounded real systems has received great interest over the years. Several methods have been published regarding these issues which are able to produce positive real or bounded real reduced models. However, none of them can guarantee that the reduced models are both positive real and bounded real at the same time. In this brief, a novel model reduction scheme is presented which focuses on preserving two possible properties of the system (positive realness and bounded realness) simultaneously. This is done by using one positive real Riccati equation and one bounded real Riccati equation in the reduction procedure. Thereafter, the gramians extracted from these Riccati equations are balanced based on the Balanced Truncation (BT) concept. Finally, a numerical example is provided to investigate the efficacy of the proposed method.